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Lab done #469

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247 changes: 228 additions & 19 deletions lab-intro-probability.ipynb
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Original file line number Diff line number Diff line change
Expand Up @@ -38,11 +38,40 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"#code here"
"from scipy.stats import binom"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.884477246621543\n"
]
}
],
"source": [
"n = 460 # tickets sold\n",
"p = 0.03 # probability of missing flight\n",
"\n",
"prob = 1 - binom.cdf(9, n, p)\n",
"\n",
"print(prob)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"About 88.1% chance that there are enough seats for everyone."
]
},
{
Expand Down Expand Up @@ -72,11 +101,30 @@
},
{
"cell_type": "code",
"execution_count": 5,
"execution_count": 3,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.48999999999999994\n"
]
}
],
"source": [
"#code here"
"p = 0.3\n",
"\n",
"prob = (1 - p) ** 2\n",
"\n",
"print(prob)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"There is a 49% probability the representative needs three or more attempts."
]
},
{
Expand Down Expand Up @@ -107,11 +155,40 @@
},
{
"cell_type": "code",
"execution_count": 6,
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"#code here"
"from scipy.stats import poisson"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.01289822084039205\n"
]
}
],
"source": [
"lam = 500\n",
"\n",
"# Probability visits exceed server capacity\n",
"prob = 1 - poisson.cdf(550, lam)\n",
"\n",
"print(prob)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"About 1.2% chance the server is overwhelmed."
]
},
{
Expand All @@ -125,9 +202,32 @@
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.2677043869515715\n"
]
}
],
"source": [
"#code here"
"lam = 500\n",
"\n",
"# probability server is overwhelmed in one hour\n",
"p_hour = 1 - poisson.cdf(550, lam)\n",
"\n",
"# probability it happens at least once in 24 hours\n",
"p_day = 1 - (1 - p_hour) ** 24\n",
"\n",
"print(p_day)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"27% probability of happening at least once during a day."
]
},
{
Expand Down Expand Up @@ -157,10 +257,40 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": []
"source": [
"from scipy.stats import expon"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.3934693402873666\n"
]
}
],
"source": [
"rate = 1/10\n",
"\n",
"prob = expon.cdf(5, scale=1/rate)\n",
"\n",
"print(prob)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"There is about a 39% chance the next customer arrives within 5 minutes."
]
},
{
"cell_type": "markdown",
Expand All @@ -173,10 +303,41 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": []
"source": [
"import math"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.22313016014842982\n"
]
}
],
"source": [
"lam = 0.1\n",
"t = 15\n",
"\n",
"prob = math.exp(-lam * t)\n",
"\n",
"print(prob)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"There's a 22% chance of an employee taking a break."
]
},
{
"cell_type": "markdown",
Expand All @@ -196,11 +357,40 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"#code here"
"from scipy.stats import norm"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.6826894921370859\n"
]
}
],
"source": [
"mu = 150\n",
"sigma = 10\n",
"\n",
"prob = norm.cdf(160, mu, sigma) - norm.cdf(140, mu, sigma)\n",
"\n",
"print(prob)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"68% of bird weight being between 140 and 160 grams."
]
},
{
Expand All @@ -219,11 +409,30 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 14,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.4511883639059735\n"
]
}
],
"source": [
"mean = 50\n",
"\n",
"prob = expon.cdf(30, scale=mean)\n",
"\n",
"print(prob)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"outputs": [],
"source": [
"#code here"
"There is about a 45.1% probability that the component fails within the first 30 hours."
]
}
],
Expand All @@ -243,7 +452,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.10.9"
"version": "3.13.11"
}
},
"nbformat": 4,
Expand Down